Asynchronous circuit implementations operating under strong constraints (DIMS, Direct Logic, some of NCL gates, etc.) are attractive due to: 1) regularity; 2) combined implementation of the functional and completion detection logics, what simplifies the design process; 3) circuit output latency is based on the actual gate delays of the unbounded nature; 4) absence of additional synchronization chains (even of a local nature). However, the area and speed penalty is rather high. In contrast to the state-of-the-art approaches, where simple (NAND, NOR, etc.) 2-input gates are used, we propose a synthesis method based on complex nodes, i.e., nodes implementing any function of an arbitrary number of inputs. Synchronous synthesis procedures may be freely adopted for this purpose. Numerous experiments on standard benchmarks were performed and the efficiency of the proposed complex gate based method is clearly shown. DIMS and Direct Logic based asynchronous designs are considered in the paper. ...